## In the figure above, what is…

## Solution:

We are given a figure, and we need to determine the value of x + y. Let’s sketch the

diagram below:

**Statement One Alone:**

x = 70

We can fill this information into our diagram.

However, we still do not have enough information to determine the value of angle y. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

Triangle ABC and triangle ADC are both isosceles triangles.

Since we do not have any information about x or y, statement two is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

Using statements one and two we know that x = 70 and that triangle ABC and triangle ADC are both isosceles triangles. Thus, we can determine that the measure of angle BAC and angle BCA within triangle ABC, are both equal to 55 degrees. However, we still do not have any information about the individual angles within triangle ADC. Without any further information we cannot determine the value of y and thus cannot determine the value of x + y.

**Answer: E**